Which of the following numbers is a multiple of 12? ${42,44,60,82,90}$
Solution: The multiples of $12$ are $12$ $24$ $36$ $48$ ..... In general, any number that leaves no remainder when divided by $12$ is considered a multiple of $12$ We can start by dividing each of our answer choices by $12$ $42 \div 12 = 3\text{ R }6$ $44 \div 12 = 3\text{ R }8$ $60 \div 12 = 5$ $82 \div 12 = 6\text{ R }10$ $90 \div 12 = 7\text{ R }6$ The only answer choice that leaves no remainder after the division is $60$ $ 5$ $12$ $60$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $12$ are contained within the prime factors of $60$ $60 = 2\times2\times3\times5 12 = 2\times2\times3$ Therefore the only multiple of $12$ out of our choices is $60$. We can say that $60$ is divisible by $12$.